Title:
Simulation of topological field theories by quantum computers

Abstract: Quantum computers will work by evolving a high tensor power of a small (e.g.
two) dimensional Hilbert space by local gates, which can be implemented by
applying a local Hamiltonian H for a time t. In contrast to this quantum
engineering, the most abstract reaches of theoretical physics has spawned
topological models having a finite dimensional internal state space with no
natural tensor product structure and in which the evolution of the state is
discrete, H = 0. These are called topological quantum filed theories (TQFTs).
These exotic physical systems are proved to be efficiently simulated on a
quantum computer. The conclusion is two-fold: 1. TQFTs cannot be used to define
a model of computation stronger than the usual quantum model BQP. 2. TQFTs
provide a radically different way of looking at quantum computation. The rich
mathematical structure of TQFTs might suggest a new quantum algorithm.